# The Algebraic Theory of Switching Circuits

## 1st Edition

**Authors:**Gr. C. Moisil

**eBook ISBN:**9781483160764

**Imprint:**Pergamon

**Published Date:**1st January 1969

**Page Count:**720

**View all volumes in this series:**International Series in Pure and Applied Mathematics

## Table of Contents

Preface to the English Edition

Preface to the Romanian Edition

Part One

1. Introduction

1. Congruences of Integers

2. Variables Associated to Elements of Switching Circuits

3. Functions

4. Polynomials Congruent with Respect to a Modulus

5. Functions Generated by Polynomials

2 . Networks with Biposition Contacts

1. Theory of Functions in ℭℱ (2)

2. Series-Parallel Networks

3. Boolean Algebras

4. Combinational Series-Parallel Networks

5. Shunt Networks

6. Simplification of Series-Parallel Networks with Biposition Contacts

3. Ideal Operation of Ordinary Relays

1. Description of the Sequential Operation

2. Characteristic Equation of an Ideal Relay

3. Analysis of the Operation of Networks with Ideal Relays

4. The Principle of Determinism

5. Synthesis of Series-Parallel Networks for Relay Operating Programmes

6. Analysis and Synthesis of Shunt Networks

7. Analysis of the Sequential Operation of Bridge Networks

4. The Operation of Bistable Relays

5. Operation of Relays with Reduced Self-Holding Current

6 . Networks with Three-Position Contacts

1. Theory of Functions in ℭℱ (3)

2. Series-Parallel Networks with Three-Position Contacts

3. Algebra of the Series-Parallel Two-Terminals with Three-Position Contacts

4. Analysis and Synthesis of Combinational Series-Parallel Networks with Three-Position Contacts

5. Antisymmetric Series-Parallel Two-Terminals with Contacts and Rectifiers

6. Three-Valued Lukasiewicz Algebras

7. Simplification of Series-Parallel Networks with Three-Position Contacts

7. Ideal Operation of Polarized Relays

1. Characteristic Equation of an Ideal Polarized Relay

2. Analysis of the Operation of Networks with Ideal Polarized Relays

3. The Principle of Determinism

4. Synthesis of Networks with Polarized Relays

5. Polarized Relays with Two Operating Positions of the Contacts

8. Actual Operation of Ordinary Relays

9. Networks with Five-Position Contacts

1. Theory of Functions in ℭℱ (5)

2. Five-Position Contacts

3. Actual Operation of a Polarized Relay

4. Actual Operation of Networks with Ordinary Relays, with Break-Before-Make and Make-Before-Break Contacts

Part Two

10. Congruences with Respect to a Double Modulus

11. Networks with Two Ordinary Relays

1. The Field ℭℱ(22)

2. Theory of Functions in ℭℱ(22)

3. Equations of the Second and Third Degree in ℭℱ (22)

4. Combinational Series-Parallel Networks with Two Push-Buttons

5. Networks with Two Ordinary Relays

6. Combinational Series-Parallel Networks with Contacts and Rectifiers

12. Networks with Three Ordinary Relays

1. The Field ℭℱ(23)

2. The Theory of Functions in ℭℱ(23)

3. Combinational Networks with Three Push-Buttons

4. Networks with Three Ordinary Relays

13. Networks with Four Ordinary Relays

1. The Field ℭℱ(24)

2. The Theory of Functions in ℭℱ(24)

3. Relations between ℭℱ(24) and ℭℱ(22)

4. Combinational Networks with Four Push-Buttons

5. Networks with Four Relays

14. Networks with Two Polarized Relays

1. The Field ℭℱ(32)

2. Theory of Functions in ℭℱ(32)

3. Combinational Networks with Three-Position Push-Buttons

4. Networks with Two Polarized Relays

15. Networks with Three Polarized Relays

1. The Field ℭℱ(33)

2. Theory of Functions in ℭℱ(33)

3. Combinational Networks with Three-Position Push-Buttons

4. Networks with Three Polarized Relays

16. Actual Operation of Networks with Two Polarized Relays

1. The Field ℭℱ(52)

2. Theory of Functions in ℭℱ(52)

3. Networks with Two Polarized Relays

17. Simultaneous Use of Several Different Fields

1. The Cartesian Product

2. Theory of Functions in ℭℱ (2) x ℭℱ (3)

3. Bistable Relays

4. Actual Operation of Ordinary Relays

5. Actual Operation of Polarized Relays

6. Working Function of a Two-Terminal having both Two-Position and Three-Position Contacts

7. Networks with Ordinary and Polarized Relays

Part Three

18. Networks with Multi-Position Contacts

1. Functions whose Domain is Finite and whose Range is a Field

2. Functions of Several Variables

3. Working Function of a Multi-Position Contact

4. Series-Parallel Connection of Multi-Position Contacts

5. Working Function of a Series-Parallel Two-Terminal with Contacts

6. Analysis of Combinational Series-Parallel Networks with Multiposition Contacts

7. Synthesis of Combinational Series-Parallel Networks with Multiposition Contacts

8. Working Function of a Series-Parallel Two-Terminal with Multiposition Contacts and Rectifiers

9. Working Function of an Antisymmetric Series-Parallel Two-Terminal with Rectifiers and Multi-Position Contacts

19. Sequential Operation of Networks with Multi-Position Contacts

1. Sequential Operation of Multi-Position Contacts

2. Locking Contacts

3. Functions whose Argument and Values are Integers

4. Discontinuous Description of Continuous Phenomena

5. Flasher Operation

20. Operation of Networks with Slow Acting Relays

1. Networks with Slow Acting Relays

2. Operation of a Pressing Installation

3. A Protection Network with Relays

21. Operation of Networks with Rotary Switches

22. Operation of Networks with Electronic Tubes

Part Four

23. General Theory of the Switching Circuits Operation

1. The General Form of the Recurrence Equation for Normally Delayed Relays

2. General Form of the Recurrence Equations in the Case of Slow Acting Elements

3. Reduction of Networks with Slow Acting Elements to Normally Delayed Networks

4. Reduction of Networks with Multi-Position Contacts to Networks with Biposition Contacts

24. Synthesis of Networks with given Operating Conditions for their Output Elements

25. Exact Programmes

1. Definition of Exact Programmes

2. Realization of an Exact Programme

3. Conditions of Compatibility

4. Lemmas of Formal Logic

5. Analysis of the Conditions of Compatibility

6. Compatible Programmes

7. Theorems on Realization

8. Simplification of an Exact Programme

9. Examples of Simplification

26. Normal Programmes

1. Definition of a Normal Programme

2. Strict Transcription of a Normal Programme

3. Transcription of an Exact Prqgramme into a Normal Programme

4. Transcription of a Normal Programme into an Exact Programme

5. Operating Conditions and Normal Programmes

6. The Problem of a Minimal Realization

7. The Reduction of an Exact Programme

27. The Technical Condition of a Proper Operation

1. Networks with Ordinary Relays

2. Difficulties

3. Networks with Polarized Relays

Part Five

28. Synonymous Networks

1. Definition of Synonymous Networks

2. Representation of Symmetric Groups

3. Systems of Linear Equations

4. Network Classification

29. Similar Networks

1. Transmutations

2. Classification of Networks with Two Push-Buttons

3. Another Method of Network Classification

30. Isomorphic Networks

1. Network Isomorphism

2. The Classification of Autonomous Networks with One Relay

3. The Classification of Autonomous Networks with Two Relays

4. Another Classification of the Autonomous Evolutions

31. Equivalent Networks

Addenda

A Survey of the Romanian Works on the Algebraic Theory of Automata

Bibliography of Romanian Literature

Books

Papers

Doctor Thesis

Circular Letters

Index

Index of the Synthesis Examples

Other Titles in the Series

## Description

The Algebraic Theory of Switching Circuits covers the application of various algebraic tools to the delineation of the algebraic theory of switching circuits for automation with contacts and relays.

This book is organized into five parts encompassing 31 chapters. Part I deals with the principles and application of Boolean algebra and the theory of finite fields (Galois fields). Part II emphasizes the importance of the sequential operation of the automata and the variables associated to the current and to the contacts. This part also tackles the recurrence relations that describe operations of the network and the principles of the so-called characteristic equations. Part III reviews the study of networks with secondary elements other than ordinary relays, while Part IV focuses on the fundamentals and application of multi-position contacts. Part V considers several topics related to circuit with electronic elements, including triodes, pentodes, transistors, and cryotrons.

This book will be of great value to practicing engineers, mathematicians, and workers in the field of computers.

## Details

- No. of pages:
- 720

- Language:
- English

- Copyright:
- © Pergamon 1969

- Published:
- 1st January 1969

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483160764